A 1 ; kg stationary bomb explodes into three | vedclass

Name: Exam Paper Generator | JEE NEET Paper Generator | Vedclass
Brand: Vedclass
Rating: 5 (35 reviews)

Question

(D) Let the total mass be $M = 1 \; kg$. The masses of the three parts are $m_1 = 0.2 \; kg$,$m_2 = 0.2 \; kg$,and $m_3 = 0.6 \; kg$ (ratio $1:1:3$).S

Vedclass · Accepted Answer

$10\sqrt{2} \; m/s$

Vedclass · Answer

(D) Let the total mass be $M = 1 \; kg$. The masses of the three parts are $m_1 = 0.2 \; kg$,$m_2 = 0.2 \; kg$,and $m_3 = 0.6 \; kg$ (ratio $1:1:3$).Since the bomb is initially stationary,the initial momentum is $0$.By the law of conservation of linear momentum,the final momentum must also be $0$.Let the velocities of the two smaller parts be $\vec{v}_1 = 30\hat{i} \; m/s$ and $\vec{v}_2 = 30\hat{j} \; m/s$.The momentum of these two parts is $\vec{p}_{12} = m_1\vec{v}_1 + m_2\vec{v}_2 = 0.2(30\hat{i} + 30\hat{j}) = 6\hat{i} + 6\hat{j} \; kg \cdot m/s$.The magnitude of this momentum is $p_{12} = \sqrt{6^2 + 6^2} = 6\sqrt{2} \; kg \cdot m/s$.For the total momentum to be zero,the third part must have momentum $\vec{p}_3 = -\vec{p}_{12}$.Thus,$m_3 v_3 = 6\sqrt{2}$.$0.6 \cdot v_3 = 6\sqrt{2}$.$v_3 = \frac{6\sqrt{2}}{0.6} = 10\sqrt{2} \; m/s$.

$A$ $1 \; kg$ stationary bomb explodes into three parts having mass ratio $1:1:3$. The parts with equal mass move in perpendicular directions with a velocity of $30 \; m/s$. What is the velocity of the third (heavier) part?

Similar Questions

An isolated rail car originally moving with speed $v_0$ on a straight,frictionless,level track contains a large amount of sand. $A$ release valve on the bottom of the car malfunctions,and sand begins to pour out straight down relative to the rail car. Is momentum conserved in this process?

$A$ bomb of mass $3.0 \, kg$ explodes in air into two pieces of masses $2.0 \, kg$ and $1.0 \, kg$. The smaller mass travels at a speed of $80 \, m/s$. The total energy imparted to the two fragments is ............. $kJ$.

$A$ gun fires a bullet of mass $50 \, g$ with a velocity of $30 \, m/s$. Because of this,the gun is pushed back with a velocity of $1 \, m/s$. The mass of the gun is .......... $kg$.

$A$ particle of mass $4m$ explodes into three pieces of masses $m, m$ and $2m$. The equal masses move along the $X$-axis and $Y$-axis with velocities $4 \text{ ms}^{-1}$ and $6 \text{ ms}^{-1}$ respectively. The magnitude of the velocity of the heavier mass is

$A$ spacecraft of mass $M$ moves with velocity $V$ in free space. It explodes and breaks into two pieces. If after the explosion,a piece of mass $m$ comes to rest,what will be the velocity of the other piece of the spacecraft?

Vedclass Test Series

Exam Paper Generator

Online Exam Module